
Quotient-Digit Selection Function
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Moreover, to satisfy the continuity condition, it is necessary to selectqj+l - k - 1
for
r w [j ] -- s k -- ulp.
Consequently,
S k - ulp < Uk_l
5.60
Since
U k
> Uk_l
Jr- ulp,
the combined restriction on Sk is
Lk < S k
< Uk_l
.qt_ ulp
5.61
For simplicity, in some cases, we use the more conservative bound
L k < s k < Uk_ 1
5.62
Consequently, the values s k have to be inside the overlap between consecutive
selection intervals, as shown in Figure 5.17. This is the basic condition required
by the quotient-digit selection functions we describe later.
The subscript k - 1 for U, in contrast ...